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Finding the Third Proportional to 729 and 797

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Solution

The third proportional to 729 and 797 is: 871.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 797 = 797 : x
  2. Step 2: Convert to fraction form
    729/797 = 797/x
  3. Step 3: Cross multiply
    729x = 797 × 797
  4. Step 4: Simplify right side
    729x = 635,209
  5. Step 5: Solve for x
    x = 635,209/729
  6. Step 6: Final answer
    x = 871.34

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.